On Some Matrix Theorems of Frobenius and McCoy
- 1 January 1953
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 5, 332-335
- https://doi.org/10.4153/cjm-1953-038-4
Abstract
McCoy, following Frobenius, studied a problem which can be described as follows. Let k be an arbitrary field, kc its algebraic closure, and any algebra of n ⨯ n matrices over k which contains the identity I . Define a canonical ordering to be a set of n mappings λ of , or of a subset of , into kc such that the sequence λ1(A),λ2(A), …, λn(A), for each A ∈ , consists of the characteristic values (roots of det(A — xI) = 0) of A, each with the right multiplicity. Define a canonical ordering to be a Frobenius ordering if, for all non-commutative polynomials f(x1, x2, … , xm) and all finite subsets A1, A2, …, Am of ,Keywords
This publication has 3 references indexed in Scilit:
- The Homomorphic Mapping of Certain Matric Algebras onto Rings of Diagonal MatricesCanadian Journal of Mathematics, 1952
- The Theory of Simple RingsAmerican Journal of Mathematics, 1943
- On the characteristic roots of matric polynomialsBulletin of the American Mathematical Society, 1936